A first-principles algebraic approach to data transformations in data cleaning: Understanding provenance from the ground up

We provide a model describing data transformation workflows on tables constructed from first principles, namely by defining datasets as structures with functions and sets for which certain morphisms correspond to data transformations. We define rigid and deep data transformations depending on whether the geometry of the dataset is preserved or not. Finally, we add a model of concurrency using meet and join operations. Our work suggests that algebraic structures and homotopy type theory provide a more general context than other formalisms to reason about data cleaning, data transformations and their provenance.